Archive for the ‘Mathematics’ Category

Attended the presentation “An excursion through flatland: Braiding interactions of anyons,” by Gavin K. Brennen, Dept. of Physics, Macquarie University, Sydney. Anyons are hypothetical particles. They interact as a function of braiding, knotting or topological relationship with other particles rather than with distance (as with other matter). Majorana fermions are an example of fermionic anyons.

Another gem by Professor Pearl and Elias Bareinboim. It identifies the external validity practice of making threats versus license. The causal mechanisms in an experimental group and the observational group influence license for external validity. There is even help for moving from an observational situation to another observational population. This is a must reading for any serious statistician or practitioner that creates statistical models and then applies them.

Requires the compilation of the included C code for the module using Microsoft Visual Studio 2008. Uses the Structural Equation Modeling software EQS software version 6.1 2006. A first step in implementing Pearl’s causality interpretation of SEM (Structural Equation Models) using graphical diagrams to encode the causality and provides a means to determine structural causality zeros and constraints. I have the trial version of the EQS software and plan on compiling the code to replicate some of the examples int he paper.

Check out the problem and solution at:http://www.data4analysis.com/3.html
It is number 22013 on the webpage.
An excel file is included to dynamically change model parameters and recompute the solution.

This paper has many very useful ideas.
One it highlights and resolves is the symmetry/asymmetry problem or paradox that exists in the fact that the linear model
in statistics has a symmetry between the independent and dependent variables which are then consequently labeled and treated differently.
Dr. Pearl traces the cause back to the equality sign in the linear model.
In one sense it is treated as an assignment equality sign as in computer science and in another sense it is treated as the equality sign in mathematics.
The solution to the paradox is found in the use of structural equation modeling and the treatment of causality.
The methodology requires the specification of causal assumptions, quries of interest and data.
The structural equation methodology results in: logical implications of the assumptions, causal inference, testable implications, statistical inference, model testing (goodness of fit) and conditional claims.
If you ever noticed and were concerned about the symmetry in the linear model and its apparent assymetry in modeling then this is a great paper to read!

I enjoyed Dr. Pearl’s talk at the Joint Statistical meetings and this paper is a great followup to that presentation.

Using the supercomputer Gibbs at the University of New Mexico I get the following timings for various number of nodes for the creation of a random Hermitian matrix and its Eigen decomposition. Each node used 16 processors. JGW_Graphic